173.

These bodies standing apart in a room lighted by a single window
will have derivative shadows more or less short according as they
are more or less opposite to the window. Among the shadows cast by
bodies of equal mass but at unequal distances from the opening by
which they are illuminated, that shadow will be the longest of the
body which is least in the light. And in proportion as one body is
better illuminated than another its shadow will be shorter than
another. The proportion n m and e v k bear to r t and v x
corresponds with that of the shadow x to 4 and y.

The reason why those bodies which are placed most in front of the
middle of the window throw shorter shadows than those obliquely
situated is:--That the window appears in its proper form and to the
obliquely placed ones it appears foreshortened; to those in the
middle, the window shows its full size, to the oblique ones it
appears smaller; the one in the middle faces the whole hemisphere
that is e f and those on the side have only a strip; that is q r
faces a b;

and m n faces c d; the body in the middle having a
larger quantity of light than those at the sides is lighted from a
point much below its centre, and thus the shadow is shorter. And the
pyramid g 4 goes into l y exactly as often as a b goes into e
f. The axis of every derivative shadow passes through 6 1/2
76
and is in a straight line with the centre of the primary
shadow, with the centre of the body casting it and of the derivative
light and with the centre of the window and, finally, with the
centre of that portion of the source of light which is the celestial
hemisphere, y h is the centre of the derived shade, l h of the
primary shadow, l of the body throwing it, l k of the derived
light, v is the centre of the window, e is the final centre of
the original light afforded by that portion of the hemisphere of the
sky which illuminates the solid body.

Footnotes

98:76 31: passa per 6 1/2 (passes through 6 1/2). The meaning
of these words is probably this: Each of the three axes of the
derived shadow intersects the centre (mezzo) of the primary shadow
(ombra originale) and, by prolongation upwards crosses six lines.

This is self evident only in the middle diagram; but it is equally
true of the side figures if we conceive of the lines 4 f, x n v
m, y l k v, and 4 e, as prolonged beyond the semicircle of the
horizon.

98:77 : Compare the diagram on Pl. IV, No. 3. In the original
this drawing is placed between lines 3 and 22; the rest, from line 4
to line 21, is written on the left hand margin.